Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - contact me Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca on Twitter Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Lumondo Photography Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Pi Art Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Hilbertonians - Creatures on the Hilbert Curve
This love's a nameless dream.Cocteau Twinstry to figure it out

Bioinformatics and Genome Analysis Course. Izmir International Biomedicine and Genome Institute, Izmir, Turkey. May 2–14, 2016


design + visualization

EMBO Journal 2011 Cover Contest

scientific image entry - a hive panel

For the EMBO Journal 2011 Cover Contest, I prepared two entries, one for the scientific category and one for the non-scientific category.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The non-scientific entry is abstract photo of fiber optics. The scientific entry was an information graphic showing a hive panel of genomic annotations in human, mouse and dog genomes. The hive panel is based on the use of the newly introduced hive plot.

About the EMBO Journal Cover Contest

The EMBO Journal non-scientific cover prize is awarded for the most interesting and beautiful image made outside the lab. Contestants may submit, for example, photos or artistic impressions of wildlife animals, plants or landscapes. Particularly welcome will also be hand or computer-generated paintings or drawings (or photographs of other works of art) related to a biological or molecular biological topic.

The EMBO Journal scientific cover prize is awarded for the most captivating and thought-provoking contribution depicting a piece of molecular biology research. Entries can include light or electron micrographs, 3D reconstructions or models of biological specimen or molecules, spectacular artefacts collected in the lab, original new views of lab equipment (but not of colleagues!), or other research-based images to be of interest to molecular biologists.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Examples of scientific cover image winners from previous years. My Circos image (top left) won the 2010 scientfic image cover category. (see more)

2011 Contest and Image Status

The 2011 winners have been announced. The scientific image winner was Heiti Paves, who submitted a confocal image of an Arabidopsis thaliana anther filled with pollen grains. The non-scientific winner was Dieter Lampl, with his "Blue Ice" photo — a glacier in Los Glaciares National Park in Patagonia.

My non-scientific entry (photo of fiber optics) received honourable mention and was included in the Favourites of the Jury gallery.


scientific image entry - a hive panel

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Four genomes — The illustration, originally part of a poster, shows syntenic relationships between human, chimpanzee, mouse and zebrafish genomes. Curved links encode sequence similarity and outer data tracks represent consensus similarity statistics and orthologous genes. The cover image shows a detail of a visualization prepared with the free genome comparison tool, Circos. (EMBO Journal - Best Scientific Cover - 2010)

In 2010 EMBO selected my submission of a large Circos figure for its cover (see right). Front page exposure of this sort has made Circos a very popular tool for visualization in genomics, and in particular, in cancer research where there is a need to illustrate differences between genomes.

It was now time to try something else — the hive panel (learn about hive plots and hive panels).

My other entry for the 2011 cover contest was a non-scientific abstract image photo of fiber optics.

Current State of Network Visualization

A large number of layout algorithms already exist to attempt to visualize networks. In an attempt to create attractive layouts, node and edge positions are optimized to minimize some fitness function, such as overlap or force (if edges are treated as springs). Unfortunately, as a result it is impossible to relate the position of a node (or the distance between any two nodes in the layout) to their connected neighbourhood in the network. This particularly holds for large networks, where nodes and edge overlap in the layout is unavoidable.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Hairballs are irrational network visualizations. Shown here are 8 different layouts of the same network — it is impossible to identify that these images correspond to the same network. More importantly, it is very difficult to extract meaningful and quantitative information from these layouts. (Hive plots solve this problem.)

The Hive Plot

Hive Plots for Networks

The hive plot is a rational approach to visualizing networks. It is designed to complement (at times, replace) the network hairball.

In a hive plot, network nodes are assigned to and placed on axes using rational rules. These rules typically are a function of local network structure around the node (connectivity, density, centrality, etc). The resulting plot is interpretable.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
In a hive plot, nodes in a network are assigned and placed on axes using properties of the node and its relationship to its neighbours. The resulting layout is rational and easily interpreted, because the rules are based on meaningful quantities. (Hive plots rationalize network visualization.)

Hive Plots for Ratios

The hive plot can be applied to visualize a large number of ratios between three or more scales.

Instead of network edges, the lines in a hive plot now correspond to an (x,y) data pair, which can be interpreted as a ratio (x/y). This approach is particularly effective when lines are drawn as ribbons, which are then stacked. This is shown in the figure below.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A hive plot can be used to visualize ratios by rendering individual ratios as stacked ribbons. The result is the circular equivalent of a stacked bar plot (Hive plots are useful for visualizing ratios.)

The resulting visualization bears resemblance to a stacked bar plot. The circular layout grants the advantage of being able to instantly compare all pair-wise comparisons between the axes (when three axes are used). This layout also gives the image a compare compact feel and is particularly suitable for tiling.

In the examples below, a 3-axis hive plot is shown with 8 ratios between each axis. The ratios are independent, in the sense that corresponding ribbons (e.g. blue) may have different thickness on either side of an axis. For example, if x:z = 2:3 and x:y = 1:3 then the ribbon on the left of the x axis will be twice as thick as on the right (see black arrow in figure below).

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
In a dual scale hive plot, each axis supports two groups of independent ribbons. Axes can be hidden (A), shown (B), or split by various amounts (C 20deg, D 30deg, E 40deg, F 60deg) to explicitly show the transition between ribbons on either side of the axis. Download high-resolution panels A B C D E F (Hive plots are useful for visualizing ratios.)

The axes in a hive plot can be arranged arbitrarily. In the figure above panels A and B show 24 ratios — 8 each between x/y, x/z, and y/x axes. In panels C-F each axis is split to create a single 6-axis plot from a dual 3-axis plot. The split axes reveal the transition between ribbons from the left and right sides.

The dual 3-axis plot appears more stylized and mathematical, whereas the single 6-axis plot is softer and organic. As the axis split distance is increased, the plots begin to look like surface density maps, which to some degree occludes the relationships between the ratio ribbons.

Comparing Genome Annotation

For each of human (hg18), mouse (mm8) and dog (canfam2) genome assemblies, UCSC annotations, available for each genome from the table browser, were used to hierarchically organize each base in the assembly using the following criteria: gene, repeat and gene+repeat. For each of these, bases were further categorized as conserved or not.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Each base in the genome assembly was assigned to one of eight disjoint categories. (More about hive plots.)

By exhaustively intersecting each of the annotation regions, the assembly was divided into disjoint segments, each with its annotation states. For example, below are a few adjacent regions from hg18 chr1 (a assembly, r repeat, c-cf conserved with dog, c-mm conserved with mouse).

...
hg 1 120,942,663 120,945,658 2,996 a r
hg 1 120,945,659 120,945,665     7 a
hg 1 120,945,666 120,947,239 1,574 a c-cf c-mm
hg 1 120,947,240 120,947,243     4 a c-cf c-mm r
hg 1 120,947,244 120,947,268    25 a c-mm r
hg 1 120,947,269 120,950,367 3,099 a r
hg 1 120,950,368 120,950,386    19 a
...

Next, the total size of regions for each combination of annotation was calculated for each pairwise combination of genomes. The second genome in the pair dictates which conservation is used. For example, for the human-mouse pair, the relative fractions of the human genome that fall into each of the categories are

hg mm a        1,839,255,050 0.643542044483869
hg mm a,c-mm     757,027,260 0.264878365091574
hg mm a,r        206,719,589 0.0723296896425132
hg mm a,c-mm,r    42,358,464 0.0148209203088807
hg mm a,g          8,139,587 0.00284798264342638
hg mm a,c-mm,g     4,435,658 0.0015520046651231
hg mm a,g,r           48,994 1.71426463814481e-05
hg mm a,c-mm,g,r      33,869 1.18505182327074e-05

thus categorizing all the 2.86 Gb of the assembled human genome. The corresponding ratios for the mouse genome are

mm hg a          1,388,193,028 0.544355712823795
mm hg a,c-hg       892,892,218 0.350132128602082
mm hg a,r          196,173,508 0.0769260237089193
mm hg a,c-hg,r      62,305,053 0.0244318411447455
mm hg a,g            6,377,904 0.00250098394691097
mm hg a,c-hg,g       4,076,727 0.00159861747416369
mm hg a,g,r             81,889 3.21113447973805e-05
mm hg a,c-hg,g,r        57,585 2.2580954586784e-05

Using these two lists, all the ratios between the human and mouse axes can be determined. For example, for the conserved/gene/non-repeat regions the ratio of human:mouse is 0.00155:0.00160 (lines are bolded above). The corresponding ribbon for this ratio is shown below.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The ratio of conserved gene regions not in repeats between human and mouse genomes. (More about hive plots.)

Category assignment into repeat, gene and conserved region was parametrized into three ranges for each criteria. These values were selected heuristically, to obtain a reasonable sample for each combination.

  • gene g1 <4kb, g2 4kb-22kb, g3 >22kb
  • repeat r1 simple, r2 LTR, r3 LINE/SINE
  • conservation c1 <45%, c2 45%-58%, c3 >58%

Given 3 parameters for each of the categories, the full comparison is represented by 27 hive plots. These plots are arranged on the cover as follows

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The ratio of conserved gene regions not in repeats between human and mouse genomes. (More about hive plots.)

The scale of the axes was logarithmic to maintain visibility of all categories.

The final cover designs for the cluster of 27 hive plots are shown below.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Final EMBO Journal cover submissions. (More about hive plots.)

news + thoughts

Gene Volume Control

Thu 11-06-2015

I was commissioned by Scientific American to create an information graphic based on Figure 9 in the landmark Nature Integrative analysis of 111 reference human epigenomes paper.

The original figure details the relationships between more than 100 sequenced epigenomes and genetic traits, including disease like Crohn's and Alzheimer's. These relationships were shown as a heatmap in which the epigenome-trait cell depicted the P value associated with tissue-specific H3K4me1 epigenetic modification in regions of the genome associated with the trait.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Figure 9 from Integrative analysis of 111 reference human epigenomes (Nature (2015) 518 317–330). (details)

As much as I distrust network diagrams, in this case this was the right way to show the data. The network was meticulously laid out by hand to draw attention to the layered groups of diseases of traits.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Network diagram redesign of the heatmap for a select set of traits. Only relationships with –log P > 3.9 are displayed. Appears on Graphic Science page in June 2015 issue of Scientific American. (details)

This was my second information graphic for the Graphic Science page. Last year, I illustrated the extent of differences in the gene sequence of humans, Denisovans, chimps and gorillas.

Sampling distributions and the bootstrap

Thu 11-06-2015

The bootstrap is a computational method that simulates new sample from observed data. These simulated samples can be used to determine how estimates from replicate experiments might be distributed and answer questions about precision and bias.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Sampling distributions and the bootstrap. (read)

We discuss both parametric and non-parametric bootstrap. In the former, observed data are fit to a model and then new samples are drawn using the model. In the latter, no model assumption is made and simulated samples are drawn with replacement from the observed data.

Kulesa, A., Krzywinski, M., Blainey, P. & Altman, N (2015) Points of Significance: Sampling distributions and the bootstrap Nature Methods 12:477-478.

Background reading

Krzywinski, M. & Altman, N. (2013) Points of Significance: Importance of being uncertain. Nature Methods 10:809-810.

...more about the Points of Significance column



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